How would someone determine the time it takes a photon to be absorbed and emitted by an atom (the refractive index)? In hydrogen for example.

By using a refractometer...

 

There are lots of other ways too.

 

That would find the classical refractive index....

Oops, I meant without experiment

Well in that case it is incredibly difficult, and relates to fermi's golden rule and a knowledge of the density of the material...

 

http://en.wikipedia.org/wiki/Fermi%27s_golden_rule

where could I find the photon propagation (measured) rate through hydrogen gas?

 

Thanks.

It's wavelength, and density related.

 

Off the top of my head I don't know, there are physical constant books which may well contain it. And there will be papers on it.

 

For the most part it's very close to 1 though.

I just found it .. It is: 1.000132 .. How could one determine the rate which photons are absorbed then emitted with this? Thanks in advance.

Well off the top of my head, you'd work out the interaction cross section, the density, and use the difference in time for travelling say 1m...

 

Then you'd have to include fermi's golden rule in there to find the most probable lifetime of the absorption state and from that find the number of absorptions required to make the time lag, and then use that to work out the number of absorptions/atom...

 

There might be an easier way to do it, I'm just thinking aloud....

Darn.. I was hoping for something easier. Lol.

 

Would it be easier (or possible) to determine the time it takes a single hydrogen atom to emit a photon from the time it's absorbed, using the refractive index? (instead of a larger quantity)

The absorptions are to virtual states, so I'm not sure if they follow rules for real absorptions. For a real electric dipole transition, the lifetime varies as [math]\frac{1}{\omega^3}[/math] so if the transitions follow this: since dispersion tells us that higher frequencies are slowed more this implies that the higher-frequency transitions happen more often, since the electron is excited for less time in each absorption.

 

I think the classical treatment is easier to understand. Higher frequencies interact more strongly.